Stability and Controller Design of Discrete-time Switched Systems Based on Transferring-dependent Lyapunov Function Approach

This paper studies stability and controller design for discrete-time switched systems with unstable subsystems under the slow/fast admissible edge-dependent average dwell time (AED-ADT) switching. Different from the previous research results, it is the first time to propose transferring-dependent convex Lyapunov function (CLF) and transferring-dependent Lyapunov function (LF). Then, considering a slow/fast AED-ADT switching scheme, some excellent stability criteria are established according to transferring-dependent CLF and transferring-dependent LF, which have less restrictiveness compared with existing results. Corresponding to the novel transferring-dependent LFs and the properties of slow/fast AED-ADT switching, the new transferring-dependent convex controller (TD-CC) and transferring-dependent ordinary controller (TD-OC) are devised to stabilize the underlying system. Finally, the effectiveness of the proposed approach is verified by two numerical examples.

Automated summary

This paper investigates the stability and controller design for discrete-time switched systems under slow/fast AED-ADT switching, proposing novel transferring-dependent Lyapunov functions and establishing excellent stability criteria. New transferring-dependent controllers are devised based on these functions to stabilize the system effectively, as verified by numerical examples.